The background art appears to have only distant relevance to this invention. In fact, there does not appear to be any prior art involving supplementary fastening devices for an ordinary type of garment hanger hook or other hooked device which is already attached to a clothesline or other linear member by being hooked to the linear member in the normal manner. Attempts have been made to solve this problem through devices which attach to the clothesline and then, in turn, suspend the hanger hook from the device itself. Examples of devices in this category are U.S. Pat. Nos. 2,092,121; 2,915,274 and 3,184,204. There have also been devices which replace or modify the garment hanger hook in order to more positively fasten the garment hanger to the clothesline, of which the following U.S. Pat. Nos. are examples: 1,690,614; 3,048,311 and 3,240,462. There have been devices which, with some modification, might be adapted to fasten a hook to a linear member as, for example, U.S. Pat. Nos. 265,171; 825,332; 1,274,280 and 2,360,164.